Abstract
A ring R with an endomorphism σ is called σ-skew McCoy, if for any zero-divisor f(x) in the skew polynomial ring R[x; σ], there exists a nonzero element with f(x)c = 0. In this note, we show that there exists a ring R and an endomorphism σ such that the matrix ring M2(R) is σ-skew McCoy. This gives a negative answer to the question posed in “A. R. Nasr-Isfahani, On semiprime right Goldie McCoy rings, Commun. Algebra 42 (2014) 1565-1570”.
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